24 Rayleigii, TJic Mechanical Principles of Flight. 



by a vertically rotating screw offers certain present advan- 

 tages. Among the most important of these are a much 

 better ensured stability, and less danger in alighting 

 owing to the absence of rapid horizontal motion. The first 

 experiments might well be made with screws driven b}' 

 electric motors, the power being supplied from the ground 

 by means of vertical wires 30 or 40 feet long. In this 

 way the necessary experience would be easily gained, 

 and most of the doubtful points settled, before a completely 

 self-contained machine was attempted. 



In natural flight rcx'olving mechanism is not, and 

 apparently could not have been, used. .Xs we all know, 

 a bird fl\-ing horizontally through still air performs the 

 necessary work by flapping his wings. The effect of a 

 reciprocating motion in modifying the action of an aero- 

 plane was, I believe, first considered in detail by Professor 

 M. Fitzgerald.* It may. be convenient to give, as 

 naturally connected with the foregoing, an outline of this 

 theory in a modificxl form, following Professor Fitzgerald 

 in assimilating the wing to a simple aeroi)lanc, upon which 

 is imposed (without rotation) a vertical reciprocating 

 motion. 



We denote by n the horizontal velocity of the plane 



supposed uniform, by v the vertical velocity at time /, by 



the inclination of the plane to the horizon at time /, 



while .S" and JF denote the area and weight as before. If 



we assume the same formula for the pressure as before, 



although the application is now to an unsteady motion, and 



further suppose that vjn and ^ are always small, we get as 



in (9) for the whole normal [)ressure upon the plane at 



time t 



uS{H'' + zr){d + vli/) (40), 



in which however v- in (/r + v") may be omitted. 



* Proc. Roy Sof., vul. Ixiv. , p. 420, 1S99. 



